Yes, I do understand what it means. My question is whether the displacement value used for the catamaran is that of the individual hull (common practice) or the total vessel displacement.

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Im sorry, but with respect, your reply tells me you don't understand. (This is why i ask the Q).

I'll explain.

Take the monohull in the graph. Now, let us split it into 2 halves down the centreline. But let us keep the 2 hulls together as if joined. In other words, as if it is still a monohull.

We run the tests and hey presto, the results same as when one hull before the split.

Now, let us move the 2 split hulls apart, lets say less than 1mm. Technically the hull is now in 2 parts, no longer one hull. If we run that model, we can pretty much safely say the tests results will be the same as when one hull, despite the less than 1mm gap.

Let us now separate the two hulls much further, lets us say 20% of the waterline length, or S/L = 0.2, and we run the test.

When the hull was 1 hull, a monohull, the displacement is say X, and the length L.

When we run the second test with the gap less than 1mm, the displacement is still X and the length is still L.

When we run the test at S/L = 0.2, the displacement is still the same, X and the length is still L. It is still the same hull but just simply split into 2 parts, that is all.

So. If we take 1 hull, a monohull and run the test it is at a displacement X. We can calculate the length-displacement ratio which is the L/D or L/Vol^(1/3). The vol in this case we can equate to the displacement ignoring the density thus vol = X. The L/D ratio is, as shown above 9.5.

So, in the 2 hulls with a gap less than 1mm, is the displacement the same, yes, = X. Therefore the L/D ratio remains the same, in this case 9.5.

If we now have the 2 hulls at S/L = 0.2, what is the displacement well, it started as 1 hull but now split into 2, so yes the displacement is still X. Thus, the L/D ratio is the same 9.5.

The whole point of this is that is the resistance of the 2 hulls (which is split from one hull) exactly twice that of the single hull??? Since the displacement X is the same and the length L is the same.

Phil Spector had the wall of sound, Ad Hoc has the wall of obfuscation, I don't know whether deliberate or unintentional. He has plenty of reputation points, but if they were awarded for clarity of explanation, they shouldn't have been !

I am afraid that this thread has descended into total obfuscation. I thought that what we were discussing was the effect of wave drag on two parallel hulls.

We all agree that a single hull makes drag inducing waves which limit its hull speed with reducing effect as the waterline L/B ratio increases.
However both the bow and stern waves still exist, only they move away from the hull at a shallower angle, and the hollow between them moves so far aft that the hull no longer has to climb out of the hole it creates in the water.
Where two hulls are situated parallel to each other, the waves interact, causing a drag inducing wave pattern.
As the hull are moved farther apart these standing waves move aft until, at a particular point, they do not interact with the hulls at all.

Early Catamarans tended to be of quite narrow overall beam, the Gougeon 32, Choy and Prout cats come to mind.
But as Cat design experience improved , overall beam/length ratios increased, which improved the hydrodynamic performance greatly, apart from the obvious improvement in R/M.
Trimarans benefitted from this as well, except the slim amas were not as bad, as in modern design they barely touch the water in light air. They also benefit more from the increase in R/M and can carry more sail. They can have a higher Bruce number. Thats why, boat for boat, they are generally faster than Cats.

The late Edmond Bruce extensively researched L/B ratios in non heeling situations. He showed that form drag only increases as the displacement increases. Skin friction drag increases as both displacement and waterline length increase. Wave induced drag is bad At low L/B ratios , but improves very
greatly from about 7/1, to 12/1 where, it practically disappears. Improvement continues until it reaches it's limit of diminishing returns at about 20/1 providing the displacement, (weight) is kept light. The super light Tornado Cat, at 20/1 is a case in point. A compromise is reached by designers of cruising Cats and Tris, usually between 8/1 to 12/1, and performance multis from 13/1 to 20/1.
Interference drag between the hulls of multis is not usually a problem these days as modern cats and tris have much wider overall beams than in the early years of multihull design.

As the hull are moved farther apart these standing waves move aft until, at a particular point, they do not interact with the hulls at all.

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Actually, the wave drag count doesn't really work that way.
The waves which a hull creates produce drag because they carry an energy. And that energy was supplied by the moving hull (which in turn got it from the propulsor).

So, the fact that above a certain speed the interfering waves' humps or hollows are left behind the vessel and are not directly acting on the vessel's demihulls means very little from the drag point of view. What counts is the total energy contained in the waves far behind the vessel, where all these deceiving local effects have been smoothed out and morphed into a regular wave train. However, it would be wrong to say that these local effects have no influence on the vessel resistance. They determine the vessel's trim for a given speed, and the trim changes the geometry of what the water sees. So the local wave effects do change the drag of the free-to-trim vessel, when compared to a one with a fixed trim. But this influence does not magically disappear as soon as the interfering waves leave the area between the hulls. Hence, the wave interference between the cat demihulls is present at all speeds - for a given hull, at some speeds it will be beneficial and for other speeds it will be detrimental for the vessel resistance.

Im sorry, but with respect, your reply tells me you don't understand. (This is why i ask the Q).

I'll explain........

And we all know the answer to that one!

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That was certainly not what I had understood! Can you give a reference for your data? I'd like to read the original source. If you explanation is the correct one for the data you've put forward then something is very wrong, because a split single hull, with corresponding flat, vertical inner sides, will not exhibit the wave interference effect on the residuary resistance that your data indicates. It would also exhibit different frictional resistance, which would introduce errors into the experiment. You could reverse them and have the flat side out, but you'd stll have frictional errors, so this would not be a sensible way to test.

I think your data comes from tests on two symmetric hulls, each hull running at the same displacement as the monohull, and the plotted data shows the residuary resistance from one of the catamaran hulls (i.e. half the total residuary resistance of the catamaran) compared to the monohull. If you have the source we could check.

My point, and the reason for my question, is that the difference seems high for a modern catamaran form, and more typical of that seen when displacement monohull forms are stretched. These forms are designed to provide stability (because they are originally monohulls) and tend to produce different waves than a typical modern cat form, which doesn't need to develop any stability and thus the form can be optimised for resistance only. In particular, the angle of the waves as they interact changes from one hull form to another. I've been looking for some good data on this for some time, hence my interest in the source of yours.

The problem of using appropriate hull forms is common for the mono-cat comparitive experimental studies I've seen, and Tom's excellent references have similar constraints on form (a Wigley form is a useful theoretical tool, but not representative of a modern fast cat hull).

If you explanation is the correct one for the data you've put forward then something is very wrong, because a split single hull, with corresponding flat, vertical inner sides, will not exhibit the wave interference effect on the residuary resistance that your data indicates....

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Seems your grasp of logic and analogies, as well as hydrodynamics, is not as good as you think!

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